scs_int solveLinSys(const AMatrix * A, const Settings * stgs, Priv * p, scs_float * b, const scs_float * s, scs_int iter) {
scs_int cgIts;
scs_float cgTol = calcNorm(b, A->n)
* (iter < 0 ? CG_BEST_TOL : CG_MIN_TOL / POWF((scs_float) iter + 1, stgs->cg_rate));
tic(&linsysTimer);
/* solves Mx = b, for x but stores result in b */
/* s contains warm-start (if available) */
accumByAtrans(A, p, &(b[A->n]), b);
/* solves (I+A'A)x = b, s warm start, solution stored in b */
cgIts = pcg(A, stgs, p, s, b, A->n, MAX(cgTol, CG_BEST_TOL));
scaleArray(&(b[A->n]), -1, A->m);
accumByA(A, p, b, &(b[A->n]));
if (iter >= 0) {
totCgIts += cgIts;
}
totalSolveTime += tocq(&linsysTimer);
#if EXTRAVERBOSE > 0
scs_printf("linsys solve time: %1.2es\n", tocq(&linsysTimer) / 1e3);
#endif
return 0;
}
int main(int argc, char **argv) {
scs_int n, m, col_nnz, nnz, i, q_total, q_num_rows, max_q;
Cone * k;
Data * d;
Sol * sol, * opt_sol;
Info info = { 0 };
scs_float p_f, p_l;
int seed = 0;
/* default parameters */
p_f = 0.1;
p_l = 0.3;
seed = time(SCS_NULL);
switch (argc) {
case 5:
seed = atoi(argv[4]);
/* no break */
case 4:
p_f = atof(argv[2]);
p_l = atof(argv[3]);
/* no break */
case 2:
n = atoi(argv[1]);
break;
default:
scs_printf("usage:\t%s n p_f p_l s\n"
"\tcreates an SOCP with n variables where p_f fraction of rows correspond\n"
"\tto equality constraints, p_l fraction of rows correspond to LP constraints,\n"
"\tand the remaining percentage of rows are involved in second-order\n"
"\tcone constraints. the random number generator is seeded with s.\n"
"\tnote that p_f + p_l should be less than or equal to 1, and that\n"
"\tp_f should be less than .33, since that corresponds to as many equality\n"
"\tconstraints as variables.\n", argv[0]);
scs_printf("\nusage:\t%s n p_f p_l\n"
"\tdefaults the seed to the system time\n", argv[0]);
scs_printf("\nusage:\t%s n\n"
"\tdefaults to using p_f = 0.1 and p_l = 0.3\n", argv[0]);
return 0;
}
srand(seed);
scs_printf("seed : %i\n", seed);
k = scs_calloc(1, sizeof(Cone));
d = scs_calloc(1, sizeof(Data));
d->stgs = scs_calloc(1, sizeof(Settings));
sol = scs_calloc(1, sizeof(Sol));
opt_sol = scs_calloc(1, sizeof(Sol));
m = 3 * n;
col_nnz = (int) ceil(sqrt(n));
nnz = n * col_nnz;
max_q = (scs_int) ceil(3 * n / log(3 * n));
if (p_f + p_l > 1.0) {
printf("error: p_f + p_l > 1.0!\n");
return 1;
}
k->f = (scs_int) floor(3 * n * p_f);
k->l = (scs_int) floor(3 * n * p_l);
k->qsize = 0;
q_num_rows = 3 * n - k->f - k->l;
k->q = scs_malloc(q_num_rows * sizeof(scs_int));
while (q_num_rows > max_q) {
int size;
size = (rand() % max_q) + 1;
k->q[k->qsize] = size;
k->qsize++;
q_num_rows -= size;
}
if (q_num_rows > 0) {
k->q[k->qsize] = q_num_rows;
k->qsize++;
}
q_total = 0;
for (i = 0; i < k->qsize; i++) {
q_total += k->q[i];
}
k->s = SCS_NULL;
k->ssize = 0;
k->ep = 0;
k->ed = 0;
scs_printf("\nA is %ld by %ld, with %ld nonzeros per column.\n", (long) m, (long) n, (long) col_nnz);
scs_printf("A has %ld nonzeros (%f%% dense).\n", (long) nnz, 100 * (scs_float) col_nnz / m);
scs_printf("Nonzeros of A take %f GB of storage.\n", ((scs_float) nnz * sizeof(scs_float)) / POWF(2, 30));
scs_printf("Row idxs of A take %f GB of storage.\n", ((scs_float) nnz * sizeof(scs_int)) / POWF(2, 30));
scs_printf("Col ptrs of A take %f GB of storage.\n\n", ((scs_float) n * sizeof(scs_int)) / POWF(2, 30));
printf("Cone information:\n");
printf("Zero cone rows: %ld\n", (long) k->f);
printf("LP cone rows: %ld\n", (long) k->l);
printf("Number of second-order cones: %ld, covering %ld rows, with sizes\n[", (long) k->qsize, (long) q_total);
for (i = 0; i < k->qsize; i++) {
printf("%ld, ", (long) k->q[i]);
}
printf("]\n");
printf("Number of rows covered is %ld out of %ld.\n\n", (long) (q_total + k->f + k->l), (long) m);
/* set up SCS structures */
d->m = m;
d->n = n;
genRandomProbData(nnz, col_nnz, d, k, opt_sol);
setDefaultSettings(d);
scs_printf("true pri opt = %4f\n", innerProd(d->c, opt_sol->x, d->n));
scs_printf("true dua opt = %4f\n", -innerProd(d->b, opt_sol->y, d->m));
/* solve! */
scs(d, k, sol, &info);
scs_printf("true pri opt = %4f\n", innerProd(d->c, opt_sol->x, d->n));
scs_printf("true dua opt = %4f\n", -innerProd(d->b, opt_sol->y, d->m));
if (sol->x) { scs_printf("scs pri obj= %4f\n", innerProd(d->c, sol->x, d->n)); }
if (sol->y) { scs_printf("scs dua obj = %4f\n", -innerProd(d->b, sol->y, d->m)); }
freeData(d, k);
freeSol(sol);
freeSol(opt_sol);
return 0;
}
